Question

The gravitational potential in a region is given by $V=(3x+4y+12z)J/kg$. The modulus of the gravitational field at $(x=1,y=0,z=3$) is

• A. $20N/kg$
• B. $13N/kg$
• C. $12N/kg$
• D. $5N/kg$

Answer 1

The correct option is B $13N/kg$

We know that the gravitational field strength is given by as$:$

$E=\overline{-V}V$

or$,$ $E=-\left[i.\left(\delta V_x/\delta x\right)+j.\left(\delta V_y/\delta y+k.\left(\delta V_z/\delta z\right)\right)\right]$

here$,$ $V=V_x+V_y+V_z=3x+4y+12z$

So$,$ we have

$E=-\left[i.\left(\delta \left(3x\right)/\delta x\right)++j.\left(\delta \left(4y\right)/\delta y+k.\left(\delta \left(12z\right)/\delta z\right)\right)\right]$

or gravitational field strength will be

$E=12+4-3=13N/kg$

hence,

option $\left(B\right)$ is correct answer.